In Part II of this book, we described the perturbations at the ‘primordial’ epoch T ~ 1 MeV, when they first become directly accessible to observation. At that stage the dominant perturbation is the curvature perturbation ζ. There may also be a tensor perturbation hij, and isocurvature perturbations Si (with i = c, b or ν).

Now we broaden the definition of ‘primordial’ and ask about perturbations at earlier times. In this chapter we see how the perturbations of light scalar fields are generated during inflation.

The idea is quite simple. Let us focus on some comoving wavenumber k. Well before horizon exit the curvature of spacetime is negligible and we are dealing with flat spacetime field theory where the particle concept should be valid. The particle number is assumed to be negligible, so that each field is in the vacuum state.

The crucial point now is that the vacuum fluctuation of a light field will ‘freeze in’ at horizon exit, to become a classical perturbation. The process was understood in the 1970s, before inflation was proposed as a physical reality, and has nothing to do with gravity. It occurs simply because the timescale a/k of the would-be vacuum fluctuation becomes bigger than the Hubble time H−1. We will see in some detail how this intuitive picture can emerge from a proper calculation.